TITLE:
Computer Simulation of Transition Regimes of Solitons in Four-Photon Resonant Parametric Processes in Case of Two-Photon Resonance
AUTHORS:
Vladimir Feshchenko, Galina Feshchenko
KEYWORDS:
Solitons, Transition Regime, Stability
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.6 No.3,
September
23,
2016
ABSTRACT: The
transition regimes of solitons in four-photon resonant processes in the case of
two-photon absorption of the fundamental radiation are numerically
investigated. The standard system of equations for the amplitudes of
probability of finding the system in state with certain energy is used to
derive the expression for the induced polarization in the nonlinear medium. As
for the equations for the amplitudes of the optical pulses, the general case is
considered in which both the amplitudes and phases are space-time dependent. We
focus on the finite difference methods and the case of simultaneously
propagating solitons at all frequencies of the interacting waves (simultons).
The obtained results indicate that upon certain threshold conditions all
interacting pulses become the solitons of Lorentzian shape. The numerical
analysis has also shown that the soliton amplitudes significantly depend on the
ratio between the nonlinear polarizability at the fundamental frequency
ω0 and that of combination
of ω0 and the trigger-field
frequency
ω1(2ω0
+ ω1). In the second part
of the paper, we apply the method of phase planes to show that at typical
values of parameters, the solitons are stable.